Recent content by Atomised

Thanks Mark & Ray for these lessons - a great help in learning to think properly.

Homework Statement I am asked to solve the following equation, giving answer in terms of k Homework Equations $$x^5 + k^2x = 0$$ The Attempt at a Solution The answer is apparently 0. What is 0. Not even sure what that means. I would have thought: divide through by x to...

Love the $$(x-0)$$ stuff thanks. .

How intriguing - what does a root having a multiplicity of two actually mean? Can a root have a multiplicity >2? Yes I see what you mean, the x-axis is kissed by the parabola but does not cross it in that region. So that happens generally when you get coincident roots? .

Homework Statement I have solved the equation $$x^3=7x^2$$ giving roots at $$x=7, x=0$$ The solutions in the book also give a specific third solution of $$x=0$$ again. I can't see the point of this unless it is to reassure the reader that there are no further solutions to look for given...

Fully acknowledge two solutions - it was hare brained of me to omit in earlier post. I will experiment with substitutions more from now on.

It is not immediately apparent to me what the advantage of making this substitution is. Is it that it makes apparent that $$z=t^2$$ and therefore $$x=t$$ Or could it be that it is suggesting the difference of two squares identity, which I cannot see how to use? .

Full Solution x_1=t\\ y_1=1/x\\ x_2=-1/t^3\\ y_2=-t^3

(x - t) (x t^3 + 1) = 0, therefore x = t, and (1) implies y = 1/t. Solved thank you very much. I am self studying and this forum is incredibly helpful.

Homework Statement Given 1) xy = 1 2) x(t^2)-y = (t^3)-1/t Express x in t, y in t 2. The attempt at a solutionx/t = [(tx+1)(td-1)] / [(t^2)-1] but I still can't separate t and x, driving me mad it is. Also subtracted 1) from 2) to obtain (t^2)x - (t^3) +1/t -1/x = 0 but no progress...

Thanks I have a better understanding of the behaviour of elementary functions now.

Sorry for unclarity. I think I should have said aα(x) + bβ(x) = γ(x). I am investigating what happens when you add and multiply equations in the context of studying simultaneous equations. All very basic stuff that I glossed over in the past. I am indeed asking for that justification yes.

Homework Statement What does it mean that basic arithmetic can be performed with two (non parallel) linear equations and that the resulting equation also intersects the same point? Proof and or anecdotal explanation would be much appreciated. Homework Equations If (α) 3y = 4x...

The 'non-understandable' was just the supposedly witty signature comment set on my PF app. Now removed.

Easy in principle. I was frustrated by my apparent inability to juggle six figure decimals (even with HP42S to help, me the world's best calculator). I have proven that the problem I am currently working on is non-understandable at x_n, for all n.